Problem 1. The current yield curve for default-free zero-coupon bonds is as follows:

Maturity(years)YTM

1 10.0%

2 11.0%

3 12.0%

1. What are the implied one-year forward rates?

2. Assume that only the expectations hypothesis explains the shape of the term structure.

If market expectations are accurate, what will the yield curve (that is, the yields to

maturity on one- and two- year zero-coupon bonds) be next year?

3. If you purchase a two-year zero-coupon bond now, what is the expected total rate of

return over the next year? What if you purchase a three year zero coupon bond? (Hint:

compute the current and expected future prices.)

1

Problem 2. A pension plan is obligated to make disbursements of $1 million, $2 million,

and $1 million at the end of each of the next three years, respectively. Find the duration of

the plan's obligations if the interest rate is 10% annually.

Problem 3. You are the manager for the bond portfolio of a pension fund. The policies of

the fund allow for the use of active strategies in managing the bond portfolio.allow for the use of active strategies in managing the bond portfolio.

It appears that the economic cycle is beginning to mature, ination is expected to ac-ination is expected to ac-

celerate, and, in an eort to contain the economic expansion, central bank policy is moving, and, in an eort to contain the economic expansion, central bank policy is moving

toward constraint. For each of the situations below, state which one of the two bonds youstate which one of the two bonds you

would prefer. Justify your answer in each case.

1. Government of Canada (Canadian pay), 4% coupon due in 2017, and priced at $101.25

(per F=$100) to yield 3.50% to maturity; or Government of Canada (Canadian pay),

4% coupon due in 2027, and priced at $95.75 (per F=$100) to yield 4.19% to maturity.

2. Commonwealth Edison, 2.75% coupon bond due in 2021, rated Baa, and priced at $81Baa, and priced at $81

(per F=$100) to yield 7.2% to maturity; or Commonwealth Edison, 93/8 % coupon bond

due in 2021, rated Baa, and priced at $114 (per F=$100) to yield 7.2% to maturity.

Problem 4. You will be paying $10,000 a year in tuition expenses for the next two years

(paid at the end of each year). Bonds currently yield 8%.

1. What is the present value and duration of your obligation?

2. What maturity zero-coupon bond would immunize your obligation?zero-coupon bond would immunize your obligation?

3. Suppose you buy a zero-coupon bond with value and duration equal to your obligation.

Now suppose that rates immediately increase to 9%. What happens to your net posi-posi-

tion, that is, to the dierence between the value of the bond and that of your tuition, that is, to the dierence between the value of the bond and that of your tuition

obligation? What if rates fall to 7%.

Problem 5. Consider the following investment strategy using European options on Ford

that expire in July. Write one call option with an exercise price of $170, and and write another

call option with an exercise price of $195. The rst call (X=$170) is currently priced at $10

and the second call (X=$195) is priced at $5.

(a) Plot the prot of this strategy

(b) What is the maximum potential prot and loss of this strategy?

(c) Why would you follow this strategy?

(d) What are the stock prices at which this strategy would break even?

Investments F303 Problem Set 2 This assignment is due by 4 PM (in a hard-copy) on the due date in Hodge Hall 6000. A drop-off box will be available at the finance department reception area on the 6th floor. Note that once the office closes, you won't be able to access the box. I will have a sign-in sheet in the box: you must copy the names on the problem set onto this sheet before you turn in your problem set. Late submissions are not be accepted and are worth 0 points. The homework will be graded mostly on completeness (refer to the syllabus for details) assuming you have shown detailed derivations of your answer. You are encouraged to work with other students (up to 4 studends including yourself). In this case, submit a single solution for your group with all members' names on it. Write both your name(s) and your section # (e.g. TR 10:30 AM). You can also work individually. You must SHOW ALL YOUR WORK in a well-organized fashion if you wish to be considered for any credit at allpartial or full. Please BE NEAT and ORGANIZED! If we cannot make sense of what you have written, it does not exist. Wherever you use a financial calculator, write down all inputs and what you are solving for. Problems 1-5 are required, problem 6 is extra credit. Problem 1. The current yield curve for default-free zero-coupon bonds is as follows: Maturity(years) YTM 1 2 3 10.0% 11.0% 12.0% 1. What are the implied one-year forward rates? 2. Assume that only the expectations hypothesis explains the shape of the term structure. If market expectations are accurate, what will the yield curve (that is, the yields to maturity on one- and two- year zero-coupon bonds) be next year? 3. If you purchase a two-year zero-coupon bond now, what is the expected total rate of return over the next year? What if you purchase a three year zero coupon bond? (Hint: compute the current and expected future prices.) 1 Problem 2. A pension plan is obligated to make disbursements of $1 million, $2 million, and $1 million at the end of each of the next three years, respectively. Find the duration of the plan's obligations if the interest rate is 10% annually. Problem 3. You are the manager for the bond portfolio of a pension fund. The policies of the fund allow for the use of active strategies in managing the bond portfolio. It appears that the economic cycle is beginning to mature, inflation is expected to accelerate, and, in an effort to contain the economic expansion, central bank policy is moving toward constraint. For each of the situations below, state which one of the two bonds you would prefer. Justify your answer in each case. 1. Government of Canada (Canadian pay), 4% coupon due in 2017, and priced at $101.25 (per F=$100) to yield 3.50% to maturity; or Government of Canada (Canadian pay), 4% coupon due in 2027, and priced at $95.75 (per F=$100) to yield 4.19% to maturity. 2. Commonwealth Edison, 2.75% coupon bond due in 2021, rated Baa, and priced at $81 (per F=$100) to yield 7.2% to maturity; or Commonwealth Edison, 93/8 % coupon bond due in 2021, rated Baa, and priced at $114 (per F=$100) to yield 7.2% to maturity. Problem 4. You will be paying $10,000 a year in tuition expenses for the next two years (paid at the end of each year). Bonds currently yield 8%. 1. What is the present value and duration of your obligation? 2. What maturity zero-coupon bond would immunize your obligation? 3. Suppose you buy a zero-coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to 9%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation? What if rates fall to 7%. Problem 5. Consider the following investment strategy using European options on Ford that expire in July. Write one call option with an exercise price of $170, and write another call option with an exercise price of $195. The first call (X=$170) is currently priced at $10 and the second call (X=$195) is priced at $5. (a) Plot the profit of this strategy (b) What is the maximum potential profit and loss of this strategy? (c) Why would you follow this strategy? (d) What are the stock prices at which this strategy would break even? 2